Text Solve the system of inequalities {2x−3<5x2−x−6≥0.\begin{cases}2x-3<5\\ x^2-x-6\ge 0.\end{cases}{2x−3<5x2−x−6≥0. Solution First: 2x<8 ⟹ x<42x<8\implies x<42x<8⟹x<4. Second: x2−x−6=(x−3)(x+2)≥0 ⟹ x≤−2 ∨ x≥3x^2-x-6=(x-3)(x+2)\ge 0\implies x\le -2\ \vee\ x\ge 3x2−x−6=(x−3)(x+2)≥0⟹x≤−2 ∨ x≥3. Intersecting with x<4x<4x<4: x≤−2 ∨ 3≤x<4.\boxed{x\le -2\ \vee\ 3\le x<4.}x≤−2 ∨ 3≤x<4.